A 7kg box sled is coasting across frictionless ice at speed of 9 m/s when a 9kg package is dropped into it from above. what is the new speed of the sled?
conservation of momentum...
7*9=(7+9)V
solve for V
To find the new speed of the sled, we can use the principle of conservation of momentum. According to this principle, the total momentum before the package is dropped is equal to the total momentum after the package is dropped.
The momentum of an object is calculated by multiplying its mass by its velocity: momentum = mass × velocity.
Before the package is dropped, the momentum of the sled is given by: momentum1 = mass1 × velocity1, where mass1 = 7 kg and velocity1 = 9 m/s.
After the package is dropped, the total mass of the system (sled + package) becomes 7 kg + 9 kg = 16 kg. Let's denote the final velocity of the sled as v.
Therefore, the momentum of the sled and package together after the package is dropped is: momentum2 = (mass1 + mass2) × v.
According to the conservation of momentum principle, momentum1 = momentum2. So we have:
mass1 × velocity1 = (mass1 + mass2) × v
7 kg × 9 m/s = 16 kg × v
Now we can solve for v:
63 kg·m/s = 16 kg × v
Dividing both sides of the equation by 16 kg:
v = 63 kg·m/s / 16 kg
Simplifying the expression:
v ≈ 3.94 m/s
Therefore, the new speed of the sled after the package is dropped into it is approximately 3.94 m/s.